Multiplayer mode is obviously in Super Smash Bros Ultimate and allows you to play coop or online against players in the whole world. One of the new features allows you to play against players having the same preferences as you.
Playing offline
You can play offline on the same console with your friends, up to 8 players, but also with several consoles, where you will have to connect two consoles.
Playing online
Matches are played with 4 players and you will be able to fight under the same rules and level. Power Smash was created for that: it's a ranking of players from all over the world.
Choosing its own rules
Before each match, you can choose your own rules, or choose nothing. Once done, the 4 players with the nearest rules will be gathered and the fight's rules will be randomly chosen between you all.
Smash Power
It's your online ranking, in the whold world. It gets higher at each victory. If you upgrade enough your Smash power, you may access the VIP Smash mode with the best players.
Additionally, you can create a private arena to play online with your friends and talk in voice chat on the Nintendo Switch Online app.
Smash Tags
It's kind of an identity card online, with your player name and a chosen color on it.
When you beat a player, you will get his Smash Tag. However, by losing, you won't lose yours. You just have to gather the most Tags by beating others.
Sending messages
As every good multiplayer game, you can send short messages to your opponents by using direction buttons of your joycons.
Play online with a friend
You also can play online with a teammate. You need a second controller and you will be able to play on the same screen against opponents from the whole world.
Spectating
You don't want to play but would rather watch and learn? You can now with the spectator mode on Nintendo Switch.
Smash World app
Whereas the Nintendo Switch Online app allows you to chat with players in your arena for example, Smash World will allow you to share videos and photos of your fights. It's free and will remain updated.